Class 9 - Frequency Polygon: Definition, Steps, Formulas & Examples

Frequency polygon is a graph of distributed data that helps us understand this data by representing it as a certain shape. Histograms and frequency polygons are very similar, but frequency polygons are better for comparing two or more sets of data. The graph is mostly a line graph that shows cumulative frequency distribution data. Let's learn about the frequency polygons graph and how to make it through some examples to get a better idea of what it means.

Table of Contents

• What is a Frequency Polygon?
• Steps to Draw a Frequency Polygon
• What is the Difference Between a Frequency Polygon and a Histogram?

What is a Frequency Polygon?

A frequency polygon is a shape made by connecting the middle points of each interval or bar of histogram. The height of the points shows how often each interval happens. I.e, its frequency. So, Frequency polygons are a type of graph that are commonly used in statistics to show how often something happens. This type of graphical representation is highly useful in studying data trends more systematically. 

Steps to Draw a Frequency Polygon

You can usually draw this kind of graph with a histogram, but you can also draw it without one. A histogram is a graph with rectangular bars that don't have any spaces. A frequency polygon graph, on the other hand, is a line graph that shows cumulative frequency distribution data. Here are two ways to make a frequency polygon from a frequency distribution:
i) By using a histogram 
ii) Without using a histogram

By using a Histogram:
First, we need to draw a histogram, and then we can draw frequency polygons by following these steps:
Step 1: Pick the class interval and write the numbers on the horizontal axes.
Step 2: Put a mark on the horizontal axes at the middle value of each interval.
Step 3: Write the class's frequency on the vertical axes.
Step 4: For each class interval, mark a point at the height in the middle of the interval that matches the frequency of that interval.
Step 5: Use the line segment to connect these points.
Step 6: The representation we got is a frequency polygon.

Without using a Histogram: Frequency polygons can also be drawn independently without drawing histograms. For this, we require the mid-points of the class-intervals used in the data. These mid-points of the class-intervals are called class-marks. To find the class-mark of a class interval, we find the sum of the upper limit and lower limit of a class and divide it by 2. 

Thus, Class-mark = Upper limit + Lower limit/2

What is the Difference Between a Frequency Polygon and a Histogram?

A frequency polygon graph is similar to a histogram, but they are not the same. You can plot a frequency polygon graph with or without a histogram. There are differences between the two graphs that are easy to see. The differences are as follows: